[M1] Bootstrap NestJS V2 backend

[rodrigolinhas]

Goal

Introduce the minimum NestJS application structure without modifying V1 behavior.

Architectural Principle

M1 must build only the infrastructure required for the first usable NestJS vertical slice. Avoid introducing architecture for hypothetical future complexity.

Expected Scope

• Create the V2 NestJS backend alongside the existing V1 code.
• Preserve the existing Express backend intact during migration.
• Configure TypeScript appropriately for NestJS without breaking root compiler configs.
• Establish development/build/start commands clearly distinguishing V1 and V2.
• Create a minimal application module (AppModule) with clean startup/shutdown hooks.
• Keep package management coherent with the current repository structure.

Acceptance Criteria

• NestJS backend can start independently.
• NestJS backend can build successfully.
• Existing Express V1 source remains intact.
• Existing React frontend remains intact.
• No authentication migration is introduced.
• No mood-entry migration is introduced.
• No PostgreSQL schema for users/entries is introduced yet unless strictly required by another approved M1 issue.
• Repository scripts clearly distinguish V1 and V2 where needed.
• Existing root build remains functional or changes are explicitly documented.

Dependencies

None.

Suggested PR

PR 1 — NestJS bootstrap